Calculus Queries (2 Viewers)

[Aplus]

But it was like basic first principles. Like differentiating x^2 - 2x from first principles. It wasn't something like...... differentiating x^-0.5.

Yeah, but I'd only use it if the question forceably said, "Use first principles..."

 

[bored of sc]

Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir³
= volume of sphere
dV/dr = 4pir²
= surface area of sphere

 

[Aerath]

Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir³
= volume of sphere
dV/dr = 4pir²
= surface area of sphere

Yes.
That's the first thing our teacher taught us when teaching us how to differentiate.

 

[tommykins]

Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir³
= volume of sphere
dV/dr = 4pir²
= surface area of sphere

Welcome to the world of volumes (if you're planning to do 4unit).

tripped me out when i realised the circumference -> area -> volume of a circle/sphere were integrals.

2pir -> pir^2 -> [pir^3]/3

 

[the-derivative]

Yes.
That's the first thing our teacher taught us when teaching us how to differentiate.

Same here.
Some people were having an argument with our teacher about the relevance of calculus and how it relates to 'real maths' (those individuals have been dropped from accelerated- thought I'd mention that) and our teacher showed us that, and that shut those people up.

I found it quite interesting as well =]

 

[12o9]

Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir³
= volume of sphere
dV/dr = 4pir²
= surface area of sphere

Whoa. That's rather hectic.

 

[Iruka]

Same here.
Some people were having an argument with our teacher about the relevance of calculus and how it relates to 'real maths' (those individuals have been dropped from accelerated- thought I'd mention that) and our teacher showed us that, and that shut those people up.

I found it quite interesting as well =]

Real maths only begins with calculus!

 

[the-derivative]

Real maths only begins with calculus!

Exactly...
Applications of Calculus to the Physical World....
Rates of Change, Exponential Growth and Decay, Simple Harmonic Motion, Projectile Motion... all seem more useful to me than knowing the s.a. of a cylinder.

 

[bored of sc]

Exactly...
Applications of Calculus to the Physical World....
Rates of Change, Exponential Growth and Decay, Simple Harmonic Motion, Projectile Motion... all seem more useful to me than knowing the s.a. of a cylinder.

But remember the surface area of cylinder can be figured out through the differentiation of the volume of a cylinder.

V = pi.r².h
dV/dr = 2.pi.r.h <---- Equals the rectangular part wrapping around shape.

Then just add on the circles that enclose the cylinder:
S.A = 2.pi.r² + 2.pi.r.h.